In 1817, 11 years after the Liverpool-born horse anatomist and painter died, a whole troop of horses went on display in London that eclipsed anything a British recorder of horseflesh might do. These horses were attributed to the ancient Greeksculptor Phidias, who probably was responsible for the design of the marble frieze taken from the Acropolis in Athens by the British diplomat Lord Elgin after paying off the Turkish rulers of Greece. Acquired by parliament for the British Museum, the frieze from the Parthenon - built at the command of Pericles in 500BC after the Persians sacked the old temples on the citadel - was regarded by Hanoverian neoclassicists as the single greatest achievement of ancient Greek art.

This judgment stands. Today, you can walk along the parade of horses in Bloomsbury and marvel. Horses have never been portrayed with more variety, character and life than they were by Greek stone carvers two and a half millennia ago. It's a cliche to call classical art "chilly", almost as cliched as calling marble "cold". The Elgin Marbles disprove both received ideas. Some horses raise their heads proudly, others blow downward furiously; one strains, another is sedate. The young men riding them - mostly robed, but some nude - turn and talk or struggle with an unruly mount. All of them, though, maintain control, finally.

Why do horses figure so largely on these stones? Why so many, in such proud array? The frieze probably depicts the Great Panathenaic procession that made its way up to the Acropolis every four years. This ideal image of the world's first democracy is typically seen as an assertion of order against the forces of chaos, the cavalcade of riders - always on the edge of breaking ranks - a triumph of hard-won harmony and balance, like the doric Parthenon itself up there in the blue sky.

I think there's a simpler explanation. The Athenians are showing off. They are boasting how well their young men can ride. The presence of these riders is a mystery - the real procession involved infantry, who are absent. The display of horsemanship seems connected to the Panathenaic games. Naked riding was an Olympic sport. There's a gratuitous, free spirit to the marble horse riders - a pride in achievement for the sake of it, just like the Greek athletic spirit the modern Olympics dimly echo. Taming and riding horses was a matter of great pride in ancient Greece. In Homer's Iliad, the hero Hector is given the epithet "tamer of horses". In his tragedy Antigone, Sophocles praises man, wonder of the world, who has tamed "shaggy-maned horses".

You see those same shaggy-maned horses portrayed, 2,000 years before the Parthenon, on the Standard of Ur. This isn't really a standard but a box, whose purpose and even original shape are unknown, discovered by British archaeologists in Iraq in the late 1920s. Its scenes, inlaid in blue lapis lazuli, red limestone and shell, are among the oldest representations of human society that exist - depicting everyday life in Mesopotamia in the third millennium BC. Horses are shown pulling chariots. No one rides them, though. The Sumerians can't make that boast.